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I'm not sure it is absolutely intended but it is at least an expected behavior: When you write f(x) = <expr>
, SageMath actually creates a "callable symbolic expression" from <expr>
(in which x
is considered as a symbolic variable). This means that <expr>
itself must initially be a symbolic expression (or anything that can be transformed into a symbolic expression). But this is not the case of divisors(n)
since divisors
is not a symbolic function applicable to a symbolic variable. Thus you must use the def ... return ...
construction, or the equivalent lambda
-expression f = lambda n: divisors(n)
.
In other words, there is a difference between a symbolic function, which is a Sage object made to represent mathematical functions (thus you can work with it, for instance derive it, integrate, etc.) and a Python function which is a function in the computer science sense, that is a subroutine. The shorthand f(x) = <expr>
is a construction for symbolic functions and not for Python functions.